willy kracht

7/27/2019 Willy Kracht

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A stochastic approach for measuring bubble

size distribution via image analysis

A solu t ion to the bubble c lusters p rob lem

W. Kracht, X. Emery, A. Egaa

ALGES laboratory, Mining Engineering Department

Universidad de Chile


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Introduction

Bubble size distribution measurement

Classical image analysis

Stochastic approach

Geometric covariogram

Results on simulated images

Conclusions

Outline


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Bubble size estimation, e.g., drift flux analysis.

It is not clear what is the role of chemistry on the model

UCT: bubbles sampled with a capillary.

Underestimation of BSD

Bubble Size Distribution (BSD) measurement


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Sampling for image technique.

Bubbles sampled from the pulp and imaged in a viewing

chamber (bubble viewer)

Bubble Size Distribution (BSD) measurement

CameraViewing chamber

Lamp

Sampling tube


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Image converted from 24-bit RGB to 8-bit gray scale and

later to a binary image.

Classical Image analysis: pre-process


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Object recognition: each set of adjacent black pixels is

recognized as an object and four cases are defined:

Classical Image analysis: segmentation

Bubble Clusters

Bubble Clusters(edge)

Single Bubbles

Single Bubbles

(edge)


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Three alternatives:

Watershed

Manual processing

Assume they are representative and neglect them

Cluster processing

Watershed Manual processing Neglect them


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The images can be modelled as a stochastic process:

A set of circular objects, with varying diameters, disposed

randomly over the area of the picture (Boolean model)

Stochastic approach


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The geometric covariogram of an object has information

of its geometric properties

Geometric covariogram of a disc (2D-bubble)

Geometric covariogram of a disc (800 pixels)


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The geometric covariogram of a distribution of discs or

bubbles is represented by the average of single

covariograms

Geometric covariogram of a distribution

BSD (5% 200p, 20% 400p, 5% 800p)BSD (100% 800p)


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The geometric covariogram of an image can be

estimated directly from the image before segmentation.

Instead of calculating the covariogram of single objects,

one calculates the probability that two points distant by a

distance h, simultaneously belong to the background of

the image.

This approach takes much shorter than classical image

analysis (1 to 10% of the time for segmentation-

watershed).

Extracting geometric properties of an image


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100 bubble images were simulated as a Boolean model

with sizes following a log-normal distribution with d10 =

1.0 mm and d32 = 1.4 mm.

Simulated images

0

3

6

9

12

15

0 1 2 3 4

Diameter, mm

N

umberfrequency,


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The 100 images are processed by both methods:

classical image analysis, neglecting bubble clusters

(left); and the stochastic approach (right).

Results

0

3

6

9

12

15

0 1 2 3 4

Diameter, mm

Numberfrequency,%

0

3

6

9

12

15

0 1 2 3

Diameter, mm

Numberfrequency,%


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Neglecting bubble clusters makes large bubbles to be

underestimated.

Indeed, in the simulation, d10 and d32 are underestimated

by 10 and 14% respectively.

The bubble surface area flux is then overestimated by

16-17%.

Results


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Both, bubble clusters and bubbles truncated by the edge

of the image should be considered.

Not considering them leads to bubble size

underestimation.

It is possible to determine the bubble size distribution

without applying classical image analysis.

If bubble clusters are not a problem, the sensor (bubble

viewer) geometry can be modified: there is no need for

the sloped window.

Conclusions


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ALGES laboratory, where the technique is being

developed.

AMTC (Advanced Mining Technology Center) for

supporting this investigation.

Acknowledgements


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A stochastic approach for measuring bubble

size distribution via image analysis

A solu t ion to the bubble c lusters p rob lem

W. Kracht, X. Emery, A. Egaa

ALGES laboratory, Mining Engineering Department

Universidad de Chile

willy kracht

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